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By Erik Mosekilde

Interacting chaotic oscillators are of curiosity in lots of components of physics, biology, and engineering. within the organic sciences, for example, one of many difficult difficulties is to appreciate how a bunch of cells or sensible devices, every one showing advanced nonlinear dynamic phenomena, can have interaction with each other to provide a coherent reaction on a better organizational point.

This publication is a advisor to the attention-grabbing new suggestion of chaotic synchronization. the themes coated variety from transverse balance and riddled basins of charm in a procedure of 2 coupled logistic maps over partial synchronization and clustering in structures of many chaotic oscillators, to noise-induced synchronization of coherence resonance oscillators. different subject matters taken care of within the e-book are on-off intermittency and the position of the soaking up and combined soaking up components, periodic orbit threshold thought, the effect of a small parameter mismatch, and assorted mechanisms for chaotic part synchronization.

The organic examples contain synchronization of the bursting habit of coupled insulin-producing beta cells, chaotic section synchronization within the strain and move law of neighboring sensible devices of the kidney, and homoclinic transitions to part synchronization in microbiological reactors.

Contents: Coupled Nonlinear Oscillators; Transverse balance of Coupled Maps; Unfolding the Riddling Bifurcation; Time-Continuous platforms; Coupled Pancreatic Cells; Chaotic part Synchronization; inhabitants Dynamic structures; Clustering of worldwide Maps; Interacting Nephrons; Coherence Resonance Oscillators.

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Additional resources for Chaotic Synchronization: Applications to Living Systems

Example text

0 1 R. 2. Regions of parameter plane where the transverse Lyapunov exponent Ax < 0. 2 shows the regions of parameter space in which Ax < 0, so that the synchronized attractor is (at least) weakly stable. The figure was obtained by performing 1000 scans of X±(e) for different values of a with a similar resolution along the e axis [26]. The stability regions clearly reflect the complexity of the bifurcation structure. In particular, we notice the irregular variation with a in the chaotic regime. , the individual map displays an attracting cycle, and the synchronized behavior is also periodic.

At both ends of this region, the in-phase period-2 cycle becomes transversely unstable. 9(a)-(c) show typical examples of the basins of attraction observed in this region. At the same time, they illustrate an interesting change in the chaotic dynamics. In Fig. 3) we have an absolutely stable two-band attractor A\ on the main diagonal. There are holes in the basin of attraction. However, these holes do not emanate from points embedded in the attractor. Hence the basin is not riddled, but has a fractal boundary.

B. A. D. Traub, Gamma Rhythms and Beta Rhythms Have Different Synchronization Properties, Proc. Nat. Acad. Sci. 97, 1867-1872 (2000). [20] F. Mormann, K. Lehnertz, P. E. Elger, Mean Phase Coherence as a Measure of Phase Synchronization and Its Application to the EEG of Epilepsy Patients, Physica D 144, 358-369 (2000). [21] K. Kaneko, Relevance of Dynamic Clustering to Biological Networks, Physica D 75, 55-73 (1994). P. Leyssac and L. Baumbach, An Oscillating Intratubular Pressure Response to Alterations in Henle Loop Flow in the Rat Kidney, Acta Physiol.

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